Learn About Craps Math and Game Strategy

Understanding the Basics of Craps Dice Probability

Craps is a dice game where players bet on the outcomes of rolls made with two six-sided dice. To understand the math behind craps, you first need to grasp how probability works with two dice. When rolling two dice, there are 36 possible combinations (6 multiplied by 6). Each combination has an equal 1 in 36 chance of occurring on any single roll.

The total of the two dice ranges from 2 to 12. However, these totals do not occur with equal frequency. A 7 can be rolled six different ways: 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1. This means a 7 occurs in 6 of the 36 possible combinations, giving it a probability of 6/36, or roughly 16.7%. In contrast, a 2 can only be rolled one way (1-1), making its probability 1/36, or about 2.8%.

Understanding which numbers come up most frequently is crucial to craps strategy. The number 7 is the most common roll, appearing once every 6 rolls on average. The numbers 6 and 8 are the second-most common, each appearing once every 6.67 rolls. The numbers 5 and 9 appear once every 9 rolls. The rarer numbers—2, 3, 11, and 12—appear far less often.

This probability distribution directly influences which bets offer better odds and which ones should be avoided. The house edge varies dramatically depending on the bet type. Some bets, like pass and don't pass, offer a house edge around 1.4%, making them among the better bets in the casino. Other bets carry house edges above 10%, meaning the casino's mathematical advantage is much larger.

Practical Takeaway: Before placing any bet in craps, memorize the likelihood of rolling each number. Knowing that 7 is the most common roll helps you understand why certain bets exist and what risks you're taking. This foundation makes all other craps strategy decisions clearer.

The Pass Line and Don't Pass Line Strategy

The pass line bet is the most fundamental wager in craps and one of the best bets available to players. When you place a pass line bet, you're betting that the shooter will win. Here's how it works mathematically: on the first roll (called the "come-out roll"), a total of 7 or 11 wins immediately, and you keep your original bet plus a matching amount. A total of 2, 3, or 12 loses immediately (these outcomes are called "craps").

If the come-out roll is 4, 5, 6, 8, 9, or 10, that number becomes the "point." The shooter then continues rolling until either rolling the point number again (you win) or rolling a 7 (you lose). The probability of winning a pass line bet overall is 49.3%, while the probability of losing is 50.7%. This means the house has only a 1.4% edge, which is excellent compared to most casino games.

The don't pass line bet is the opposite. You win if the come-out roll is 2 or 3, you push (tie) if it's 12, and you lose if it's 7 or 11. If a point is established, you win if a 7 rolls before the point repeats. The don't pass bet also has a house edge around 1.4%, making it equally favorable mathematically. However, don't pass bettors must often lay more money than they stand to win on certain point numbers.

The mathematical advantage of these bets comes from their alignment with actual probability. Both pass and don't pass bets pay 1 to 1 odds, which fairly reflects the probability of winning. Because the math works in your favor compared to other bets, experienced players focus heavily on these two wagers and avoid making many other types of bets at the same table.

Practical Takeaway: If you're new to craps, stick primarily with pass line or don't pass line bets. The house edge is low, the bets are simple to understand, and the math behind them is sound. Building your craps strategy on these foundation bets gives you the best mathematical chance of prolonging your play.

Come and Don't Come Bets Explained

Come and don't come bets are similar to pass and don't pass bets, but they're placed after the point is already established. This is an important distinction because it changes when the bet resolves and how you should think about the math involved. A come bet is essentially a new pass line bet placed on a roll that occurs after the point is set.

When you place a come bet, the very next roll becomes a new "come-out roll" for your specific wager. If that roll is 7 or 11, your come bet wins immediately at 1-to-1 odds. If it's 2, 3, or 12, your come bet loses. If it's 4, 5, 6, 8, 9, or 10, that becomes your "come point," and you win if that number rolls again before a 7 appears. The house edge on come bets is also around 1.4%, matching the pass line.

Don't come bets work inversely. You win if the roll is 2 or 3, push on 12, and lose on 7 or 11. If a come point is established, you win if 7 rolls before that number repeats. Like don't pass, the house edge is about 1.4%. The mathematics of come and don't come bets are identical to their pass/don't pass counterparts—the only real difference is timing and which roll initiates them.

Many players use multiple come bets to create several action points simultaneously. For example, with one come point of 5 and another of 9, you're essentially betting on multiple numbers. However, this increases complexity and doesn't improve your overall odds. Each individual bet carries the same 1.4% house edge regardless. The value of come bets lies mainly in maintaining engagement throughout longer rolls rather than improving mathematical outcomes.

Practical Takeaway: Come and don't come bets offer the same mathematical value as pass and don't pass, but they let you create action on multiple rolls. Use them if you enjoy having several wagers in play, but understand that adding more bets doesn't change your mathematical advantage—it only adds complexity and usually increases how much money you're wagering at once.

Understanding Odds Bets and Their Mathematical Advantage

One of the most important concepts in craps strategy is the "odds bet," also called "taking odds" or "laying odds." This supplemental bet allows you to back up your pass line, don't pass, come, or don't come bets with additional money at true odds—a situation where the house gains no mathematical advantage. Odds bets are among the only wagers in a casino where you can achieve a 0% house edge.

After a point is established, you can place an odds bet in addition to your original wager. The amount you can bet depends on casino rules, but common limits are 2x, 3x, or 5x your original bet (some casinos allow up to 10x or 20x). For a pass line bet where the point is 4 or 10, true odds are 2-to-1, meaning you risk $2 to win $1. For points of 5 or 9, true odds are 3-to-2. For points of 6 or 8, true odds are 6-to-5.

The reason odds bets matter mathematically is that they reduce your overall house edge on your combined bets. If you place a $10 pass line bet and then add a $10 odds bet on a point of 6, your combined wagers now carry a lower house edge than your pass line bet alone. While both parts of the bet have different individual characteristics, the weighted average house edge drops significantly. Taking the maximum odds allowed effectively minimizes the casino's mathematical edge on your money.

Don't pass players also use odds bets, but they "lay odds" instead of "take odds." Laying odds means you're betting that a 7